On generalized quasi Einstein standard static spacetimes

In the present paper, first, we characterize the standard static spacetimes satisfying certain Ricci-Hessian class type equations, such as generalized quasi Einstein manifolds, m-quasi Einstein manifolds, (m,ρ)-quasi Einstein manifolds, and gradient Ricci solitons. Then, we obtain some necessary and sufficient conditions about the existence of certain vector fields on the standard static spacetime. We also characterize the m-quasi Einstein standard static spacetimes admitting concurrent or parallel vector fields and get several physical properties of such spacetimes. At last, we construct non-trivial examples of m-quasi Einstein spacetimes verifying our results.